Related papers: Deformations and elements of deformation theory
Mark all vertices on a curve evolving under a family of curves obtained by intersecting a smooth surface M with the 1-parameter family of planes parallel to the tangent plane to M at a point p. Those vertices trace out a set, called the…
In the first one of these two lectures, I give an introductory review of phase transitions in finite temperature field theories. I highlight the differences between theories with global and local symmetries, and the similarities between…
We give the facet description of the deformation cones of graph associahedra and nestohedra, generalizing the classical parametrization of the family of deformed permutahedra by the cone of submodular functions. When the underlying building…
This work deals with the presence of defect structures in generalized sine-Gordon models. The models are described by periodic potentials, with substructure having one, two, three or more distinct topological sectors, with multiplicity one,…
In this work we investigate two distinct extensions of the deformation procedure introduced in former works on deformed defects. The first extension deals with the use of deformation functions which can assume complex values, and the second…
We review the main features of models where relativistic symmetries are deformed at the Planck scale. We cover the motivations and links to other quantum gravity approaches. We describe in some detail the most studied theoretical…
This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic…
This pedagogical review presents the Shell Correction Method (SCM) and variants thereof, appropriate for describing shape deformations and electronic shell effects, energetics and decay pathways of metal-cluster fragmentation processes…
Informed by our understanding of the tt-geometry of permutation modules, we investigate the proper definition of the `stable permutation category' of a finite group. Then we prove that this category decomposes over cyclic and generalized…
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…
In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
We develop a general deformation theory of objects in homotopy and derived categories of DG categories. The main result is a general pro-representability theorem for the corresponding deformation functor.
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and polyvector fields. We then introduce the formalism of…
We consider isospectral deformations of quantum field theories by using the novel construction tool of warped convolutions. The deformation enables us to obtain a variety of models that are wedge-local and have nontrivial scattering…
In this work we further develop a nonlocal calculus theory (initially introduced in [5]) associated with singular fractional-type operators which exhibit kernels with finite support of interactions. The applicability of the framework to…
Hierarchical (first-order) structured deformations are studied from the variational point of view. The main contributions of the present research are the first steps, at the theoretical level, to establish a variational framework to…
We describe constructing solutions of the field equations of Chern-Simons and topological BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations)…
A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for…